Sentence examples for existed a concept from inspiring English sources

He argued this species had gone extinct and no longer existed, a concept that was not widely accepted at the time.

This asserts: there exists a concept G such that for every object x, x falls under G if and only if x is odd and greater than 5.

If the partition of (Delta ^mathcal {I}) by (sim _{Sigma ^dag,Phi ^dag,d,mathcal {I}}) is consistent with X, then there exists a concept C of (mathcal {L}_{Sigma ^dag,Phi ^dag,d,}) such that (C^mathcal {I}= X).

If there exists a concept C of (mathcal {L}_{Sigma ^dag,Phi ^dag,d,}) such that (X = C^mathcal {I}), then the partition of (Delta ^mathcal {I}) by (sim _{Sigma ^dag,Phi ^dag,d,mathcal {I}}) is consistent with X.   2.

Similarly, for each (1 le i le m'), there exists a concept (D'_i) of (mathcal {L}_{Sigma ^dag,Phi ^dag,j,}) such that (y" in (D'_i)^{mathcal {I}"}) but (t'_i notin (D'_i)^{mathcal {I}'}).

If the partition of (Delta ^mathcal {I}) by (sim _{Sigma ^dag,Phi ^dag,d,mathcal {I}}) is consistent with X, then there exists a concept C of (mathcal {L}_{Sigma ^dag,Phi ^dag,d,}) such that (C^mathcal {I}= X).  .

If there exists a concept C of (mathcal {L}_{Sigma ^dag,Phi ^dag,d,}) such that (X = C^mathcal {I}), then the partition of (Delta ^mathcal {I}) by (sim _{Sigma ^dag,Phi ^dag,d,mathcal {I}}) is consistent with X.

For each (1 le i le m), there exists a concept (D_i) of (mathcal {L}_{Sigma ^dag,Phi ^dag,j,}) such that (y" in D_i^{mathcal {I}"}) but (t_i notin D_i^mathcal {I}).

Thus, for every (1 le i le n), there exists a concept (C_i) in (mathcal {L}_{Sigma ^dag,Phi ^dag,j,}) such that (C_i^mathcal {I} y)) holds, but (C_i^{mathcal {I} y(y'_i)) does not.

Then: 1. if there exists a concept (C) of (mathcal {L}_{Sigma ^dag,Phi ^dag }) such that (X, =, C^mathcal {I}) then the partition of (Delta ^mathcal {I}) by (sim _{Sigma ^dag,Phi ^dag,mathcal {I}}) is consistent with (X),   2.

For each (1 le i le m) and (1 le j le n), since (Y_i) and (Y'_j) are different equivalence classes of (equiv _{Sigma ^dag,Phi ^dag,d,mathcal {I}}) (the same as (sim _{Sigma ^dag,Phi ^dag,d,mathcal {I}})), there exists a concept (C_{i,j}) of (mathcal {L}_{Sigma ^dag,Phi ^dag,d,}) such that (Y_i subseteq C_{i,j}^mathcal {I}) and (Y'_j cap C_{i,j}^mathcal {I}= emptyset ).